If you're not certain about her history, there is the possibility that she may be pregnant and she may be close to kidding.
You can have her ultrasounded to determine if she is pregnant or you can wait for her to kid.
If she is not pregnant, it is possible that she is having a false pregnancy and may be producing milk.
Even if her udder is swollen, don't milk her. You don't want to remove the first milk (colostrum) if she is pregnant.
If she's not pregnant, she will dry up in about a week if you do not milk her.
She definitely isn't pregnant, and she's been like this for a few weeks. I thought it would dry up too. How long should I give it?
Each doe is different. It will probably take her longer than most to dry up. As long as she is eating and drinking normally, all you can do is wait a bit longer. It may take another two weeks before her udder begins to shrink.